I have sales data on 200 grocery brands who add a fair trade symbol to their product packaging (6 months before they become a member, and 6 months after they become a member). I also have data on all other grocery brands that do not add it.
How can I model this taking into account self-selection?
I have thought about Difference-in-Difference (or matching), but any control group of products (or matched product in the same category) will be affected by the product adding the fair trade symbol, I assume this makes it impossible as any control group is also affected by the treatment?
Would it make sense to do a before/after for each product (sales after - sales before), or is this still subject to self-selection?
Can I estimate a selection equation? However, I have multilevel data (product within a brand, within categories, within a retailer, across time). Is this feasible?
I know I could use 2SLS, but I can't find any valid instrument.